Synthetic Commodity strategies

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Brief discussion on forward contracts: 

Let us take two parties A and B in a commodity market. The party A is the buyer and party B is the seller in forward market. 

This means party A has agreed to buy in future or taken a long position and party B has taken a short forward position. 

Let us suppose the price of the commodity per bushel = $961.54 cents per bushel (Spot price or S₀)

Let us suppose that they agreed into a forward contract and fixed the strike price (X) = $1000

The forward price after a time T is denoted with F_(0,T).

Today’s price is denoted as S₀ and forward price of the commodity is denoted with F_(0,T).

Please understand that the price of the commodity at time “T” can take any price. That is decided by the market demand and supply factors at time “T”. 

Suppose the price of the commodity at time T is $1050. In that case, the trader with long position will buy as per the forward contract at $1000 cents per bushel from party B and sell in the market for $1050, to gain $50 cents per bushel. The gain is generally denoted as (S_T – X), where S_T is the spot price of the commodity at time T_T and “X” is the agreed price for the long forward position holder.

Suppose the price of the commodity at time T is $950. In that case, the trader with long position will have to buy as per the forward contract at $1000 cents per bushel. He is at loss, because, the same commodity is available in the market for $950.

This means that forward contracts do have the volatility risk of the underlying assets. The agreed time to maturity of the contract will also have an impact on forward contracts.

How do we reduce such affects?

Let us purchase a zero coupon bond with future maturity par value of $1000, with remaining maturity of one year. Let us suppose the price of the bond as of now (T₀) is $961.54 and on maturity the bond will pay us par value of $1000.

Let us now enter into a long forward contract where the agreed forward price is equal to $1000. Please understand at the time of entering into a forward contract, there is no cash outflow or expenses (Initiation level).

Let us suppose the present risk-free rate in the market is 5% per annum (USD).

Let us denote the forward price of the commodity as F_(0,T). This means the forward contract is for the period T₀ to T_T and F_(0,T) is equal to $1000 ( as per the above discussion).

What is the present value of this forward contract?

It is equal to S₀ x e^-rt = $1000 x e^{-0.05 x 1}  = $961.54 

(where, 0.05 is the risk free rate and 1year is the remaining period for the future contract to mature).

This means the present value of the forward contract is equal to = $961.54

Also the present price paid for buying the zero coupon bond is also equal to = $961.54

Therefore at time T₀:

The cost of buying the zero coupon bond =The present value of forward contract = F_(0,T) x e^-rt and it is equal to $961.54

At maturity or at time T_T, the total pay off of the long forward contract and the zero coupon bond will be as below:

(S_T – X) [ pay-off or gain from the long forward contract] + $1000 from bond par value 

 “$1000 from bond par value” can be written as F_(0,T). Because the par value of the bond is equal to the agreed forward price.

Or the agreed forward price “X”  = F_(0,T) = Bond par value.

Therefore the total pay-off from the long forward contract and bond can be written as:

(S_T – F_(0,T)) + F_(0,T) = S_T

The above strategy is known as synthetic commodity creation.

I summarize this strategy as below to create a synthetic commodity as:

Long zero coupon bond + Long forward contract = Synthetic commodity price at time T.

In this the par value of the bond is equal to the agreed forward price of the contract. Such strategies are used to avoid the impact of price volatilities on the underlying assets.